Two-relaxation-time regularized lattice Boltzmann model for convection-diffusion equation with spatially dependent coefficients

Abstract

In this paper, a new two-relaxation-time regularized (TRT-R) lattice Boltzmann (LB) model for the convection-diffusion equation (CDE) with spatially dependent coefficients is proposed. Within this framework, we first derive a TRT-R collision operator (CO) by constructing a new regularized procedure through the high-order Hermite expansion of non-equilibrium part. Then, a first-order discrete-velocity form of discrete source term is introduced to improve the accuracy of the source term. Finally, a new first-order space-derivative auxiliary term is proposed to recover the correct CDE. To assess this model, we simulated non-homogeneous convection-diffusion problems with adjustable diffusion intensity in both two and three dimensions. The findings indicate that the newly introduced source terms markedly enhance the model's precision and stability under varying time steps, grid resolutions, diffusion scaling coefficients, and magic parameters. The adoption of the TRT-R CO leads to a significant error reduction compared to the classic BGK CO in most scenarios. Furthermore, the influence of the magic parameter on the performance of the TRT-R CO was investigated. Beyond this, the study also confirms the efficacy of the TRT-R CO in eliminating numerical slip when enforcing Dirichlet boundary conditions with a halfway bounce-back scheme, thereby providing further evidence of the algorithm's advantages.